List of publications and preprints

Analysis, PDE, and Spectral Geometry

• S. Looi. A counterexample to the Berger–Coburn conjecture. arXiv. 

• S. Looi. Unbounded symbols, heat flow, and Toeplitz operators. arXiv.

• S. Looi, D. Sher. The heat trace for domains with curved corners. arXiv.

• B. Dodson, S. Looi. Quantitative scattering for the energy-critical wave equation on asymptotically flat spacetimes. arXiv.

• S. Looi, E. Sussman. Asymptotics in all regimes for the Schrödinger equation with time-independent coefficients. arXiv. To appear in Analysis and PDE. 

• S. Looi, P. Isett. A proof of Onsager's Conjecture for the SQG equation. arXiv.

• S. Looi, H. Xiong. Asymptotic expansions for semilinear waves on asymptotically flat spacetimes. arXiv.

• S. Looi. Sharp Pointwise Decay for Quasilinear Waves on Black Hole Spacetimes. arXiv.

• S. Looi. Quantitative Decay for Nonlinear Wave Equations on Dynamic Spacetimes, with Sharpness for Power-Type Nonlinearities. arXiv.

• S. Looi. Sharp Pointwise Decay for the Energy-Critical Wave Equation on Dynamical, Asymptotically Flat Spacetimes. arXiv.

• S. Looi, M. Tohaneanu. Global existence and pointwise decay for nonlinear waves under the null condition, Dyn. Partial Differ. Equ. 23 (2026), no. 3, 225–268. arXiv.

• S. Looi. Pointwise decay for the wave equation on nonstationary spacetimes. J. Math. Anal. Appl. arXiv:2105.02865.

• S. Looi, M. Tohaneanu. Scattering for critical wave equations with variable coefficients. Proc. Edinb. Math. Soc. 64(2), 298–316 (2021). arXiv.

In preparation (draft available upon request):

• S. Looi. Sharp pointwise asymptotics for nonlinear and linear waves in even dimensions. 

• S. Looi. Spectral stability and local energy decay. 

Machine Learning

• Data for Mathematical Copilots: Better Ways of Presenting Proofs for Machine Learning. arXiv.
    S. Frieder, J. Bayer, S. Looi, J. Loader, J. Berner, K. M. Collins, A. Juhász, F. Ruehle, S. Welleck, G. Poesia, R.-R. Griffiths, A. Weller, A. Goyal, T. Lukasiewicz, K. Buzzard, and T. Gowers.

• What's the Magic Word? A Control Theory of LLM Prompting. arXiv.
    A. Bhargava, S. Looi, C. Witkowski, M. Thomson.

• Mathematical Datasheets for Datasets.
    S. Frieder, S. Looi, K. M. Collins, T. Lukasiewicz. Link.

•  AI Impact on Human Proof Formalization Workflows, accepted at NeurIPS MATH-AI workshop 2025.
      K. M. Collins, S. Frieder, J. Bayer, J. Loader, J. Lim, P. Song, F. Zaiser, L. Zhou, S. Li, S. Looi, J. Hernandez-Orallo, J. B. Tenenbaum, C. Freer, U. Bhatt, A. Weller, V. Chen, I. Sucholutsky

• Humanity's Last Exam. arXiv, Nature. (Contributing author.)

Thesis

• S. Looi. Some problems in quasilinear and damped wave equations. Honors Thesis, UC Berkeley (2017).

• S. Looi. Asymptotic behavior of hyperbolic partial differential equations. PhD Thesis, University of Kentucky.